Problem 156 - A Complete Resource Book in Chemistry for JEE Main

Question

In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen? (a) \(3 \longrightarrow 2\) (b) \(5 \longrightarrow 2\) (c) \(4 \longrightarrow 1\) (d) \(2 \longrightarrow 5\)

Step-by-Step Solution

Answer

The transition is from 5 to 2.

Step 1: Understanding the Bohr Model

The Bohr model describes the hydrogen atom's electron transitions between energy levels, which emit light at specific wavelengths. These emissions form a series of spectral lines classified into various series depending on the ending level of the transition.

Step 2: Identifying the Series

The Balmer series of hydrogen involves transitions where the electron falls to the second energy level ( _{low} = 2). The first line of the series corresponds to the transition from n=3 to n=2.

Step 3: Finding the Third Line from the Red End

Each line in the Balmer series corresponds to a transition from higher energy levels to n=2. The third line corresponds to the transition from n=5 to n=2, because the sequence starts from 3 to 2, then 4 to 2, and the third is 5 to 2.

Step 4: Conclusion

Thus, the third line from the red end in the Balmer series involves the transition from the 5th to the 2nd energy level in the hydrogen atom.

Key Concepts

Bohr Model

The Bohr Model, introduced by Niels Bohr in 1913, is a fundamental concept in understanding atomic structure, particularly for the hydrogen atom. It describes how electrons orbit the nucleus in specific paths or "shells." These paths are at certain fixed distances from the nucleus, meaning electrons have quantized energy levels. This model was groundbreaking because it linked atomic structure with the emission or absorption of light.
This model explains why atoms emit light at specific wavelengths. When an electron jumps from a higher energy level to a lower one, it releases energy in the form of light. The Bohr Model was successful in predicting the wavelengths of the hydrogen spectral lines but was later replaced by more complex quantum mechanical models for elements with more than one electron.

• The Bohr model features quantized orbits or "energy levels".
• Electrons transition between these levels by absorbing or emitting photons.
• The model is especially accurate for the hydrogen atom.

Balmer Series

The Balmer Series is a set of spectral lines corresponding to visible light emitted when electrons in a hydrogen atom transition to the second lowest energy level, known as n=2. It is a part of the hydrogen emission spectrum. Comprised of several lines, each corresponds to an electron falling from a higher energy level.
The series was named after Johann Balmer, who in 1885 discovered a formula to predict the wavelengths of the visible lines in the hydrogen spectrum. The Balmer series is particularly important because it includes lines visible to the naked eye, making it easier to study.

• Includes visible wavelengths: red, blue, and violet lines.
• Results from transitions to the second energy level (n=2).
• Essential for understanding atomic spectra and light emission processes.

Electron Transition

Electron transitions are crucial in defining the spectral lines of an atom. They occur when an electron moves between different energy levels within an atom. In the Bohr Model, these transitions involve quantized energy changes, meaning that electrons can only move between specified orbits.
When transitioning from a higher to a lower energy level, electrons emit photons, creating emission lines in the spectrum. Conversely, when absorbing energy, they jump to a higher level. In hydrogen, these transitions help produce several series, such as Lyman, Balmer, and Paschen, each with unique characteristics.

• Causes the emission or absorption of light.
• Characterized by quantized energy changes.
• Defines the nature of various spectral series.

Energy Levels

Energy levels in atoms refer to the fixed distances where electrons are likely to be found orbiting the nucleus. In the Bohr Model, these levels are illustrated as concentric circles around the nucleus. Each energy level is associated with a specific amount of energy, and each corresponds to an integer value often represented by n.
The concept of energy levels helps explain why atoms absorb or emit photons only at specific energies. The difference in energy between two levels determines the wavelength of light emitted or absorbed during an electron transition. Understanding energy levels is crucial for deciphering the hydrogen spectrum and the behavior of electrons within other atoms.

• Represent quantized electron orbits within an atom.
• Each level corresponds to a specific energy state.
• Key to understanding atomic spectra and chemical bonding.